Nonparametric estimation of reliability function using the kernel density estimation method

Analysis of data from an accelerated life test employs a model. Such a statistical model for an accelerated life test consists of a life distribution that represents the scatter in product life and a relationship between life and stress. In this study, the Coffin-Manson relationship is used to model fatigue failure of metals subject to thermal cycling. Generally there are two statistical methods for estimating reliability of objects (life distribution). One is a parametric approach and the other is a nonparametric one. The parametric method assumes that the underlying distribution function belongs to a fixed distribution family indexed by a finite number of parameters. The unknown parameters are then estimated from the data. On the other hand, the nonparametric method does not specify a particular family of distributions. The major difficulty of the parametric approach arises at the stage of model specification. Correct specification of the underlying model is crucial for successful application of the parametric approach. Incorrect specification yields severe model bias and this cannot be compensated in any degree by accurate parameter estimation. In this paper, we provide a nonparametric method to estimate the life distribution under normal usage from accelerated life test data